Question

Resolva as seguintes equações exponenciais​

Answer 1

a)

$625^{2x}~=~\dfrac{1}{125^{x-14}}\\\\\\\left(5^{4}\right)^{2x}~=~\dfrac{1}{\left(5^3\right)^{x-14}}\\\\\\\left(5^\right)^{4\,.\,2x}~=~\dfrac{1}{\left(5\right)^{3\,.\,(x-14)}}\\\\\\5^{8x}~=~\left(5^{-1}\right)^{3x-42}\\\\\\5\!\!\!\backslash^{8x}~=~5\!\!\!\backslash^{-3x+42}\\\\\\8x~=\,-3x+42\\\\\\11x~=~42\\\\\\\boxed{x~=~\frac{42}{11}}$

b)

$\sqrt{121^x}~=~1331^{-6+2x}\\\\\\121^{\frac{x}{2}}~=~\left(11^3\right)^{-6+2x}\\\\\\\left(11^2\right)^{\frac{x}{2}}~=~11^{3\,.\,(-6+2x)}\\\\\\11\!\!\!\!\backslash^{\,2\,.\,\frac{x}{2}}~=~11\!\!\!\!\backslash^{\,-18+6x}\\\\\\x~=~-18+6x\\\\\\6x-x~=~18\\\\\\\boxed{x~=~\frac{18}{5}~~ou~~3,6}$